The increasing demands for processor performance are driving system designers to adopt multiprocessors. In this paper, we study global fixed priority scheduling in multiprocessor real-time systems and introduce a technique for improving the schedulability. The key idea is to construct execution dependency for selected tasks to leverage slack time and reduce the interference between high-priority and low-priority tasks. Thus, more lower-priority tasks are enabled to be scheduled. Further, we provide a response time analysis method which takes the execution constraint of tasks into consideration. Extensive simulation results indicate that the proposed approach outperforms existing work in terms of acceptance ratio.